We've now defined MTF, but realize that we've only defined MTF at a single point in the image. The MTF curve at the center will be normally higher then the curve at the edge, which will itself normally be higher then the curve at the corner. Some authors give an "MTF" value to a lens which is some sort of weighted average across the whole image. While this may have some value, it's about the same as describing the Mona Lisa by it's average color!
Now it's not quite that bad since the MTF "map" will usually be symmetrical and peak in the center of the frame, but a badly assembled lens may well show asymmetric behavior that a single number misses and even if the lens is symmetric a single number doesn't tell you how MTF varies across the frame. A lens with high center MTF and low edge MTF may have the same "average" MTF as a lens that has a medium MTF value all across the frame.
MTF is a very powerful measure of lens performance. It can be used, for example, to calculate the effects of defocus or other aberrations on the image. However plots such as the ones presented earlier are for a single point in the image. Each point will have its own MTF curve! There's an alternative way to plot MTF data and that's to plot MTF at a given spatial frequency as a function of the distance from the center of the image. Such a plot is shown below. The data is for a Canon EF20-35/2.8L lens at 20mm.
Blue lines are for f8, black lines for f2.8
Solid lines are radial measurements, dashed lines are tangential measurements
Thick lines are for 10 lines/mm, thin lines are for 30 lines/mm
Image taken from “Lens Work” published by Canon.
As you can see, things get quite complicated quite quickly – and this plot only shows data for two apertures at two spatial frequencies and two target orientations (radial and tangential lines). MTF varies significantly across the frame and the lens shows significant astigmatism (difference between radial and tangential MTF). Radial lines are those that point towards the center of the frame, Tangential lines are those at right angles to radial lines. If you think of a spoked wheel with the hub in the center of the frame, the spokes would correspond to radial lines, while the rim of the wheel would be made up of tangential lines.
So what does it show? Well...
Now take the above plot and try to assign a single number to describe it! Giving the lens a "7/10" or "3.5 stars" really doesn't come close to describing the characteristics of the image quality
One problem with using MTF plots to judge image quality is that it's very difficult for the average user to correlate MTF plots with image quality. MTF is a purely objective measurement and is ideal for the exact scientific measurement of the optical performance of a lens but it doesn't take into account any aspects of human vision – which after all is what we use to look at an image – and that's where SQF comes in.